Finite Group Databasebeta

← #25124103

Subgroups — #25124103

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582863C211yesmaximal, characteristic, complemented
5C2×#14582759C211yesmaximal, characteristic, complemented
6#19135795C212yesmaximal, complemented
7#19135788C212yesmaximal, complemented
8#19135781C212yesmaximal, complemented
9#19135774C212yesmaximal, complemented
10#19134316C211yesmaximal, characteristic, complemented
11C2×C43×#525C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43—21no—
17#14582942—24no—
18C2×#13063258C2212yescomplemented
19C2×#13063256C2212yescomplemented
20#14582900—24no—
21#14582900—24no—
22C2×#13063249C2212yescomplemented
23C2×#13063249C2212yescomplemented
24C2×#13063246C2212yescomplemented
25C2×#13063246C2212yescomplemented
26#14582863—24no—
27C2×C22⋊(C43⋊C8)C2212yes—
28C2×C22⋊(C43⋊C8)C2212yes—
29#14582759—21no—
30#14582759—21no—
31#14582759C2212yes—
32#14582759C2212yes—
33C2×C43⋊#95—21no—
34#14582661C2212yescomplemented
35#14582661C2212yescomplemented
36C22×#41×C43C2211yescharacteristic
37C24×C4×C43C2211yescharacteristic
38C43×#525—24no—
39C43×#525—24no—
40C2×#123×C43—21no—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#121×C43C2211yescharacteristic
44C2×#121×C43C2211yescharacteristic
45C2×#120×C43—21no—
46C2×C4×D4×C43—21no—
47C2×C4×D4×C43—21no—
48C2×#117×C43C2211yescharacteristic
49C23×Dic43—21no—
50C23×Dic43—21no—
51C2×#10621877—22no—
52C2×#10621877—22no—
53C2×#10621877—22no—
54C2×#10621877—22no—
55C2×#10621877—22no—
56C2×#10621877D414yescomplemented
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2312yes—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—22no—
62C2×C4⋊Dic43—22no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2312yes—
66C2×C4⋊Dic43C2312yes—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—44no—
70#13063258—24no—
71#13063256—24no—
72#13063249—24no—
73#13063249—24no—
74#13063246—24no—
75#13063246—24no—
76C22⋊(C43⋊C8)—24no—
77C22⋊(C43⋊C8)—24no—
78C43⋊#95—22no—
79C43⋊#95—22no—
80C25×C43D411yescharacteristic
81C2×#41×C43—22no—
82C2×#41×C43—22no—
83C2×#41×C43—22no—
84C2×#41×C43—22no—
85C2×#41×C43—22no—
86C2×#41×C43D414yes—
87C22×Q8×C43C2311yescharacteristic
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43C2311yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43—22no—
94C23×C4×C43—22no—
95C23×C4×C43—22no—
96C23×C4×C43—22no—
97C23×C4×C43—22no—
98C23×C4×C43—22no—
99C23×C4×C43D411yescharacteristic
100C23×C4×C43D411yescharacteristic
101C23×C4×C43D411yescharacteristic
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105#123×C43—28no—
106C22⋊Q8×C43—22no—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109C22⋊Q8×C43—22no—
110#121×C43—22no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—22no—
114#120×C43—28no—
115C4×D4×C43—28no—
116C4×D4×C43—28no—
117#117×C43—22no—
118#117×C43D414yes—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43—21no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43—22no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43—21no—
135C24×C43—41no—
136C24×C43—41no—
137C24×C43C2×D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140#41×C43—28no—
141#41×C43—28no—
142#41×C43—44no—
143#41×C43—44no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D412yes—
150C2×D4×C43—24no—
151C2×D4×C43—24no—
152C2×D4×C43—21no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43C2×D412yes—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—24no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—44no—
191C22×C4×C43—44no—
192C22×C4×C43—42no—
193C22×C4×C43—44no—
194C22×C4×C43—42no—
195C22×C4×C43—44no—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43#4112yes—
203C22×C4×C43#4112yes—
204C22×C4×C43#4112yes—
205C22×C4×C43C2411yescharacteristic
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—42no—
209C22×Dic43—42no—
210C22×Dic43—42no—
211C22×Dic43—42no—
212C22×Dic43—42no—
213C22×Dic43—42no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C2×D412yes—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—24no—
221C22⋊C4×C43—24no—
222C22⋊C4×C43—24no—
223C22⋊C4×C43—24no—
224C22⋊C4×C43—24no—
225C42×C43—24no—
226C22⋊Dic43—44no—
227C22⋊Dic43—44no—
228C4⋊Dic43—22no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43—42no—
233C4⋊Dic43—42no—
234#10621877—28no—
235#10621877—44no—
236C2×C43⋊C8—22no—
237C2×C43⋊C8—22no—
238C2×C43⋊C8—22no—
239C2×C43⋊C8—22no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8C2×D414yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—28no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43#12012yes—
273C23×C43#12112yes—
274C23×C43#12312yes—
275C23×C43AGL(1,ℤ/8)12yes—
276C23×C43#13712yes—
277C23×C43C22×D411yescharacteristic
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—41no—
281Q8×C43—41no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—48no—
285D4×C43—48no—
286D4×C43—48no—
287D4×C43—41no—
288D4×C43—41no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—44no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—44no—
314C2×C4×C43—44no—
315C2×C4×C43—48no—
316C2×C4×C43#12012yes—
317C2×C4×C43#12114yes—
318C2×C4×C43#12114yes—
319C2×C4×C43#12112yes—
320C2×C4×C43#12314yes—
321C2×C4×C43#12312yes—
322C2×C4×C43#12414yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—84no—
336C2×Dic43—84no—
337C43⋊C8—24no—
338C43⋊C8—42no—
339#23482—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—416no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43#39414yes—
369C22×C43C2×#12011yescharacteristic
370C22×C43C2×#12111yescharacteristic
371C22×C43C2×#12311yescharacteristic
372C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C43C2×#13711yescharacteristic
374C22×C43#57511yescharacteristic
375C22×C43#57511yescharacteristic
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43#39414yes—
382C4×C43C2×#12111yescharacteristic
383C4×C43C2×#12111yescharacteristic
384C4×C43C2×#12311yescharacteristic
385C4×C43C2×#12411yescharacteristic
386Dic43—82no—
387Dic43—82no—
388C2×#525D4311yescharacteristic
389C2×#428—431no—
390C2×#417—431no—
391C2×#417—431no—
392C2×#407—431no—
393C2×#380—431no—
394#2036—432no—
395#2035—432no—
396#2034—432no—
397#2033—432no—
398#1736—431no—
399C2×C43—24no—
400C2×C43—42no—
401C2×C43—42no—
402C2×C43—82no—
403C2×C43C2×#39411yescharacteristic
404C2×C43#300611yescharacteristic
405C2×C43#300711yescharacteristic
406C2×C43#305511yescharacteristic
407C2×C43#305611yescharacteristic
408C2×C43#309211yescharacteristic
409C2×C43#309311yescharacteristic
410C22×#41C2×D4311yescharacteristic
411C24×C4C2×D4311yescharacteristic
412C22×M16—431no—
413C22×M16—431no—
414#525—24no—
415#525—24no—
416C2×#123—21no—
417C2×C22⋊Q8C2×D4311yescharacteristic
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×#121C2×D4311yescharacteristic
420C2×#121C2×D4311yescharacteristic
421C2×#120—21no—
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×#117C2×D4311yescharacteristic
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C22⋊C4—861no—
428#428—864no—
429C2×#107—432no—
430C2×#106—432no—
431#417—864no—
432#417—864no—
433C2×#103—432no—
434C2×#103—432no—
435C2×#102—432no—
436C2×#102—432no—
437#407—864no—
438C2×C22⋊C8—432no—
439C2×C22⋊C8—432no—
440#380—432no—
441#380—432no—
442#380—861no—
443#380—861no—
444C2×#95—861no—
445#340—432no—
446#340—432no—
447C43#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D4311yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D4314yes—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4C22⋊D4311yescharacteristic
470C23×C4C22⋊D4311yescharacteristic
471C23×C4C22⋊D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C2×M16—434no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—862no—
481C22×C8—432no—
482C22×C8—432no—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117C22⋊D4314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—432no—
500C2×C4⋊C4—432no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—862no—
516C2×C22⋊C4—1724no—
517C2×C42—21no—
518#107—864no—
519#106—864no—
520#103—864no—
521#103—864no—
522#102—864no—
523#102—864no—
524C22⋊C8—864no—
525C22⋊C8—864no—
526#95—862no—
527#95—862no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×C22⋊D4311yescharacteristic
537C24C2×C22⋊D4311yescharacteristic
538C24C2×C22⋊D4311yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D4312yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×C22⋊D4312yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4D4×D4312yes—
604C22×C4#1062190012yes—
605C22×C4#1062190012yes—
606C22×C4#1062190012yes—
607C22×C4C2×C22⋊D4311yescharacteristic
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4312yes—
611C22×C4C2×C22⋊D4312yes—
612C22×C4C23×D4311yescharacteristic
613M16—868no—
614M16—1724no—
615C2×C8—434no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8—862no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—862no—
626C4⋊C4—862no—
627C4⋊C4—862no—
628C4⋊C4—862no—
629C4⋊C4—1722no—
630C4⋊C4—1722no—
631C4⋊C4C2×C22⋊D4312yes—
632C4⋊C4C2×C22⋊D4312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1306329412yes—
672C23#1306329712yes—
673C23#1306330612yes—
674C23#1306335012yes—
675C23#1306335512yes—
676C23C22×C22⋊D4311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—3444no—
716C2×C4—3444no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4#1306329412yes—
724C2×C4#1306329614yes—
725C2×C4#1306329712yes—
726C2×C4#1306329714yes—
727C2×C4#1306330612yes—
728C2×C4#1306330614yes—
729C2×C4#1306331214yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C22×C22⋊D4311yescharacteristic
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4C2×#1062190011yescharacteristic
735C2×C4C2×#1062190011yescharacteristic
736C8—864no—
737C8—1722no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1458281314yes—
767C22C2×#1306329411yescharacteristic
768C22C2×#1306329711yescharacteristic
769C22C2×#1306330611yescharacteristic
770C22C2×#1306335011yescharacteristic
771C22C2×#1306335511yescharacteristic
772C22#1458369711yescharacteristic
773C22#1458369711yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3442no—
780C4—3442no—
781C4#1458281314yes—
782C4C2×#1306329611yescharacteristic
783C4C2×#1306329711yescharacteristic
784C4C2×#1306330611yescharacteristic
785C4C2×#1306331211yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1458281311yescharacteristic
791C2#1914384711yescharacteristic
792C2#1914385511yescharacteristic
793C2#1914421611yescharacteristic
794C2#1914422711yescharacteristic
795C2#1914451511yescharacteristic
796C2#1914452411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#525C2
socleC23×C43C22×D4
hypercenterC2×#525D43
hypocenterC43#23482
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
2. C2×#14582900C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582863C2semidirect
5. C2×#14582759C2semidirect
6. #19135795C2semidirect
7. #19135788C2semidirect
8. #19135781C2semidirect
9. #19135774C2semidirect
10. #19134316C2semidirect
18. C2×#13063258C22semidirect
19. C2×#13063256C22semidirect
22. C2×#13063249C22semidirect
23. C2×#13063249C22semidirect
24. C2×#13063246C22semidirect
25. C2×#13063246C22semidirect
34. #14582661C22semidirect
35. #14582661C22semidirect
56. C2×#10621877D4semidirect
447. C43#23482semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145829422
C2×#145829002
C2×#145828632
C2×#145827592
#191357952
#191357882
#191357812
#191357742
#191343162
C2×C43×#5252
#2348243